In Patent Document 1, there is disclosed a technique to regenerate a NOx trap catalyst arranged in an exhaust passage of a diesel engine. In this Patent Document 1, when the NOx trap catalyst is to be regenerated, an excess air factor in a cylinder is caused to lower up to a first excess air factor by means of an intake air throttle valve and an EGR. Then, after the excess air factor in the cylinder has reached the first excess air factor, an amount of fuel to be injected into the cylinder is increased, so that the excess air factor in the cylinder is caused to lower up to a second excess air factor at which the regeneration is performed.    [Patent Document 1] Japanese patent application laid-open No. 2004-52561